2009/07/29 by A. Matthew Smith, Lev Kaplan, L. Kaplan · 9 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Chaotic #Chaotic systems #Computer science #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hamiltonian system #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Scientific Research and Discoveries #Semiclassical physics #Simple (philosophy) #Standard map #Statistical physics #Theoretical and Computational Physics #nlin.CD
paper · pdf · doi:10.1103/physreve.80.035205
published in Physical Review E 80(3), 035205 (American Physical Society) · 5 pages, 3 figures
arxiv created 2009/07/29 · openalex publication_date 2009/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss a modification to random matrix theory (RMT) eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard RMT and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations and show how the approach leads to a significant improvement in the accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.